Multiple Input Multiple Output (MIMO) systems are becoming popular in wireless and wireline communications to leverage aspects of intersymbol interference to potentially increase the bandwidth efficiency of existing spectra. In the case of wireless systems, radio waves do not propagate simply from transmit antenna to receive antenna, but bounce and scatter randomly off objects in the environment. This scattering is known as multipath, as it results in multiple copies or images of the transmitted signal arriving at the receiver via different scattered paths. In conventional wireless systems, multipath represents a significant impediment to accurate transmission, because the images can arrive at the receiver at slightly different times, causing destructive intersymbol interference and leading to corruption or loss of the information borne by these images.
Using the BLAST MIMO wireless approach first proposed by G. J. Foschini in 1996, however, it is possible to exploit multipath, in that the scattering characteristics of the propagation environment are leveraged to enhance, rather than degrade, transmission accuracy. See G. J. Foschini, “Layered Space-Time Architecture for Wireless Communication in a Fading Environment When Using Multiple Antennas”, Bell Lab Technical Journal, Vol. 1, No. 2, Autumn 1996. This is done by treating multiple scattering paths as separate parallel subchannels, each capable of bearing distinct data. As proposed by Dr. Foschini, BLAST operates by splitting a discrete outbound datastream into multiple substreams and using an array of transmitter antennas to simultaneously launch the parallel substreams. All the substreams are transmitted in the same frequency band, so spectrum is efficiently utilized. Since the outbound data is being sent in parallel over multiple antennas, the effective transmission rate is increased in approximate proportion to the number of transmitter antennas used.
Another array of antennas is used to pick up the multiple transmitted substreams and their scattered images at the BLAST receiver. Each receive antenna picks up all of the incident transmitted substreams superimposed as observed components of the received signal vector, not separately. However, if the multipath scattering is sufficiently rich, then the multiple substreams are all scattered slightly differently, since they originate from different transmit antennas that are located at different points in space. These scattering differences allow the substreams to be identified and recovered from the observed components of the received signal vector.
In particular, the BLAST receiver signal processor(s) view the observed component signals constituting the received signal from all the receiver antennas simultaneously, first extracting the strongest substream, then proceeding with the remaining weaker signals, which are easier to recover once the stronger signals have been removed as a source of interference. Again, the ability to separate the substreams depends on the slight differences in the way the different substreams propagate through the environment. Thus, through BLAST, a multipath wireless channel is capable of bearing an enormous capacity of recoverable information, particularly in rich multipath scattering environments.
In Dr. Foschini' original proposal, now known as diagonal BLAST or D-BLAST, enormous transmission capacities are realized through combining multi-element transmit and receive antenna arrays with an elegant diagonally layered inter-substream coding structure in which coded information blocks are dispersed across diagonals in space-time (known as space-time codes). In theory, this architecture permits transmission rates to grow linearly with the number of antennas used (assuming MT transmit antennas and MR receive antennas, where MT=MR) and can approach 90% of Shannon capacity. However, the complexities involved in implementing D-BLAST space-time coding currently limits its use to situations where maximum spectral efficiency is required, without regard for transceiver complexity or cost.
A simpler version of D-BLAST called vertical BLAST or V-BLAST has therefore been proposed by Dr. Foschini and colleagues at Bell Labs. See, e.g. P. W. Wolniansky et al., “V-BLAST: An Architecture for Realizing Very High Data Rates Over the Rich-Scattering Wireless Channel”, invited paper, Proc. ISSSE-98, Pisa, Italy, Sep. 29, 1998. Like D-BLAST and BLAST techniques generally, the outbound datastream is split into plural substreams and transmitted in parallel across plural transmitter antennas. However, unlike D-BLAST, no inter-substream space-time coding is performed, resulting in a much simpler and practical vector encoding process for the outbound datastream. Instead, an individual QAM transmitter-antenna pair is provided for transmitting each substream (MT transmitters total), and each substream is symbol encoded independently of the other substreams. These transmitters may be collectively thought of as a vector-valued transmitter, where components of each transmitted MT×1 column vector are symbols drawn from e.g. a QAM constellation. MR receive antennas are used, where MT≦MR.
V-BLAST's lack of inter-substream space-time coding and associated redundancy benefits does reduce the spectral efficiencies compared to D-BLAST. Nevertheless, where MT≦MR and channel conditions result in “rich scattering”, the V-BLAST architecture similarly offers capacity increases which progress approximately linearly with increases in the number of deployed transmitter-antenna pairs.
The secret behind V-BLAST lies in the use of successive interference cancellation demodulation techniques at the receiver, similar to those employed in multi-user communication systems like DS-CDMA. The observed datastream at the receiver, which is composed of the superposition of the MT transmitted substreams, can be demodulated through successive interference cancellation and nulling to recover all the transmitted substreams. Proper demodulation and recovery of the transmitted datastream hinges critically in being able to determine the proper order in which the transmitted substreams should be demodulated. Described more fully in Foschini, such optimal substream ordering involves selecting the remaining substream with the best signal-to-noise ratio as the demodulation candidate at each iteration of the demodulation process.
As such, this form of V-BLAST demodulation, known as zero-forcing substream detection, is similar to zero-forcing decision feedback equalization (ZF-DFE). Accordingly, it is similarly effected by the noise-enhancement problem observed in zero-forcing equalizers as well as the error propagation problems characterized by decision feedback equalizers, as is well known in the art. Because of these drawbacks, recursive minimum mean-squared error estimation (MMSE) substream detection, based on MMSE decision feedback equalization used in adaptive antenna arrays, has been instead been proposed and utilized in a number of V-BLAST implementations in order to address the limitations of the zero-forcing techniques, including noise enhancement issues. See e.g. Wolniansky, and also G. D. Golden et al., “Detection algorithm and initial laboratory results using V-BLAST space-time communication architecture”, Electronic Letters, Vol. 35, No. 1, January 1999. However, regardless of whether V-BLAST zero-forcing or MMSE substream detection is used, a computation of the Moore-Penrose pseudo-inverse of a successively deflating or decomposing matrix channel transfer function H is required for each parallel substream. Moreover, pseudo-inverse matrix computation (or simply “matrix inversion”) is required to initiate optimal substream ordering per datastream.
It should be appreciated that matrix inversion is a computationally complex and expensive operation and therefore not very attractive to implement though hardware, including application specific integrated circuits (ASICs).
In the past few years, research has been initiated in generally developing MMSE solutions which are computationally less complex and avoid the need for matrix inversion operations. This research started with the seminal paper on Multi-staged Nested Weiner Filters (MSNWF) by Goldstein, Reed and Scharf (J. S. Goldstein et al., “A Multistage Representation of the Weiner Filter Based on Orthogonal Projections”, IEEE Transactions on Information Theory, Vol. 44, No. 7, November 1998, incorporated herein fully by reference). This paper revealed a novel interpretation of the Weiner-Hopf solution was revealed, along with an inversion free method for computing the same. While the motivation behind this work was to design simple reduced rank estimators, the idea has since been detailed in M. L. Honig et al., “Performance of Reduced-Rank Linear Interference Suppression”, IEEE Transactions on Information Theory, Vol. 47, No. 5, July 2001, also incorporated herein fully by reference, which proposes a simplified MMSE demodulator for DS-CDMA based downlinks. Therefore, it would be desirable to develop matrix inversion-free demodulation techniques for BLAST and other types of MIMO communications systems.